Problem: What is the value of the following logarithm? $\log_{49} 7$
Explanation: If $b^y = x$ , then $\log_{b} x = y$ Notice that $7$ is the square root of $49$ That is, $\sqrt{49} = 49^{1/2} = 7$ Thus, $\log_{49} 7 = \dfrac{1}{2}$.